Computer Science / Mathematical Software

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Matrix Inversion Using Cholesky Decomposition

Matrix Inversion Using Cholesky Decomposition

๋ณธ ๋…ผ๋ฌธ์€ ํ–‰๋ ฌ ์—ญํ–‰๋ ฌ ๊ณ„์‚ฐ์—์„œ ์ฝœ๋ ˆ์Šคํ‚ค ๋ถ„ํ•ด์™€ LDL ๋ถ„ํ•ด์˜ ํ™œ์šฉ ๋ฐฉ๋ฒ•์„ ๊ฐœ์„ ํ•˜์—ฌ ์—ฐ์‚ฐ ํšจ์œจ์„ฑ์„ ํ–ฅ์ƒ์‹œํ‚ค๋Š” ์ƒˆ๋กœ์šด ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ œ์‹œํ•œ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๊ธฐ์กด ์•Œ๊ณ ๋ฆฌ์ฆ˜์— ๋น„ํ•ด 16 17%์˜ ์—ฐ์‚ฐ ํšŸ์ˆ˜๋ฅผ ์ค„์ด๋Š” ํšจ๊ณผ๋ฅผ ๋ณด์—ฌ์ฃผ๋ฉฐ, ํŠนํžˆ ์ค‘๊ฐ„ ๊ฒฐ๊ณผ ๊ณ„์‚ฐ์„ ํ”ผํ•˜๋Š” ๋ฐฉ๋ฒ•๋ก ์ด ํ•ต์‹ฌ์ด๋‹ค. ์ฝœ๋ ˆ์Šคํ‚ค ๋ถ„ํ•ด์™€ LDL ๋ถ„ํ•ด ์ฝœ๋ ˆ์Šคํ‚ค ๋ถ„ํ•ด๋Š” ์–‘์˜ ์ค€๋Œ€์นญ ํ–‰๋ ฌ์„ ํ•˜์‚ผ๊ฐ ํ–‰๋ ฌ๊ณผ ๊ทธ ์ „์น˜ ํ–‰๋ ฌ๋กœ ๋ถ„ํ•ดํ•˜๋Š” ๊ธฐ๋ฒ•์œผ๋กœ, ์—ฐ์‚ฐ ๋ณต์žก๋„๊ฐ€ O(nยฒ) ์ด๋ฉฐ ์ˆ˜์น˜์ ์œผ๋กœ ์•ˆ์ •์ ์ด๋‹ค. ์ด ๋ฐฉ๋ฒ•์€ ์†Œํ”„ํŠธ์›จ์–ด ๊ตฌํ˜„ ์‹œ ์ƒ์‚ผ๊ฐ ํ–‰๋ ฌ์„ ์„ ํ˜ธํ•˜๋ฉฐ, C ํ”„๋กœ๊ทธ๋ž˜๋ฐ ์–ธ์–ด์™€ ํ˜ธํ™˜๋œ๋‹ค. LDL ๋ถ„

Mathematical Software Computer Science
Some Software Packages for Partial SVD Computation

Some Software Packages for Partial SVD Computation

1. ์ตœ์ ํ™”๋œ PROPACK PROPACK์€ ๋ถ€๋ถ„ SVD ๊ณ„์‚ฐ์„ ์ˆ˜ํ–‰ํ•˜๋Š” ๋ฐ ๋„๋ฆฌ ์‚ฌ์šฉ๋˜๋Š” ๋„๊ตฌ๋กœ, ์ฃผ๋กœ ํ•ต ๋…ธ๋ฆ„ ์ตœ์†Œํ™” ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด ํ™œ์šฉ๋ฉ๋‹ˆ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” PROPACK์˜ ์„ฑ๋Šฅ์„ ํ–ฅ์ƒ์‹œํ‚ค๊ธฐ ์œ„ํ•ด ๊ทธ๋žŒ ์Šˆ๋ฏธํŠธ ์ง๊ตํ™” ๊ณผ์ •์„ ์žฌ๊ตฌ์„ฑํ•˜์—ฌ 15%์—์„œ 20%๊นŒ์ง€ ์†๋„๋ฅผ ๋†’์˜€์Šต๋‹ˆ๋‹ค. ์ด ์ตœ์ ํ™”๋œ ๋ฒ„์ „์€

Mathematical Software Mathematics Computer Science

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